Create image effect in Cycles as FNAF / video noise effect
I'd do this effect in compositing by adding a noise texture. Create a noise texture and play with the settings until you have something you like. You probably will want to stretch it in X direction a good amount, otherwise you'll get boring TV noise...

To mix the texture with the render output, you could add them together. Also try a color mix node between the render and white with the (inverted) noise image as factor.

If compositing doesn't work, put the texture on a plane and attach it in front of the camera. In the material of that plane, the black of the texture should get transparent.

To animate it, animate either the seed or the UV coordinates.

EDIT

Just tried it out myself by compositing this effect over the default cube. Some tips:


I used a clouds texture for the noise. The default noise texture didn't want to get scaled properly
Adding the effect was not such a good idea. Mix works better
The clouds texture needs a color ramp to increase the contrast
Blurring the texture (after the coloramp) can improve the result
You should use multiple effect textures with different size and strength or use the one texture multiple times
Animation can be done by creating an offset vector with the time input and some love
If you use multiple textures, animate them in different directions


ANOTHER EDIT

Here my node setup with the result in the backdrop: 

I used the same texture three times, you can see its settings on the right. The combine RGBA node is just another way to input the scale vector so that you can see its values. Do not use transform/scale nodes instead because this will look bad if you are not scaling down enough. The texture on the bottom is the basic noise, it will also work alone without the others. The texture in the middle adds some really small noise. It is only stretched by factor 3. The noise setup at the top gives some of the bigger artifacts.

To animate it, put an RGBA node into the texture offset and animate it as usual.